Do you know at what point in the writing of LOTR the war ended?
Tolkien repeatedly declared there were no allegorical or political metaphors in his writing, but it is difficult to see how the ending of the most monumental man-made event in human history could not have affected the chronicle of Middle Earth. There must be evidence, even if it is only of a subconscious influence, of events in the 20th century on the timescapes of fantasy.